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RefractionAngle::usage="RefractionAngle[\!\(\*SubscriptBox[\(\[Theta]\), \(i\)]\),\!\(\*SubscriptBox[\(n\), \(i\)]\),\!\(\*SubscriptBox[\(n\), \(j\)]\)] Calculates refraction angle from normal in medium j at the boundary of mediem i and j using Snell's Law.";

FresnelA::usage="FresnelA[\"coefficient\",\!\(\*SubscriptBox[\(\[Theta]\), \(i\)]\),\!\(\*SubscriptBox[\(n\), \(i\)]\),\!\(\*SubscriptBox[\(n\), \(j\)]\)] 
calculates Fresnel amplitude coefficient for \!\(\*SubscriptBox[\(\[Theta]\), \(i\)]\) angle of incidence from normal in medium i at a planar boundary between medium i and medium j with refractive indices \!\(\*SubscriptBox[\(n\), \(i\)]\) and \!\(\*SubscriptBox[\(n\), \(j\)]\). Angle of Refraction \!\(\*SubscriptBox[\(\[Theta]\), \(j\)]\) is internally calculated using Snell's law. Eqs. 8-11.

\"coefficient\" = \"rs\" or \"rp\" for reflection
\"coefficient\" = \"ts\" or \"tp\" for transmission

FresnelA[\"coefficient\",\!\(\*SubscriptBox[\(\[Theta]\), \(i\)]\),\!\(\*SubscriptBox[\(\[Theta]\), \(j\)]\),\!\(\*SubscriptBox[\(n\), \(i\)]\),\!\(\*SubscriptBox[\(n\), \(j\)]\)] is FresnelA with \!\(\*SubscriptBox[\(\[Theta]\), \(j\)]\) specified.";

RefractionMv::usage="RefractionM[\"pol\",\!\(\*SubscriptBox[\(\[Theta]\), \(v - 1\)]\),\!\(\*SubscriptBox[\(\[Theta]\), \(v\)]\),\!\(\*SubscriptBox[\(n\), \(v - 1\)]\),\!\(\*SubscriptBox[\(n\), \(v\)]\)] gives the matrix of refraction at interface v of a thin film system for \"pol\"-polarized input beam. Eq. 6. 

\"pol\" = \"s\" or \"p\" ";

PhaseMv::usage="PhaseM[\[Omega],\!\(\*SubscriptBox[\(\[Theta]\), \(v\)]\),\!\(\*SubscriptBox[\(n\), \(v\)]\),\!\(\*SubscriptBox[\(d\), \(v\)]\)] gives the phase matrix of layer v. Eq. 12";

AbelesS::usage="AbelesS[\"pol\",\[Omega],{{\!\(\*SubscriptBox[\(\[Theta]\), \(0\)]\),\!\(\*SubscriptBox[\(n\), \(0\)]\)},{\!\(\*SubscriptBox[\(\[Theta]\), \(1\)]\),\!\(\*SubscriptBox[\(n\), \(1\)]\),\!\(\*SubscriptBox[\(d\), \(1\)]\)}..{\!\(\*SubscriptBox[\(\[Theta]\), \(k\)]\),\!\(\*SubscriptBox[\(n\), \(k\)]\),\!\(\*SubscriptBox[\(d\), \(k\)]\)},{\!\(\*SubscriptBox[\(\[Theta]\), \(k + 1\)]\),\!\(\*SubscriptBox[\(n\), \(k + 1\)]\)}}] calculates the total system transfer matrix at frequency \[Omega] with specified material refaction angles \!\(\*SubscriptBox[\(\[Theta]\), \(i\)]\), refractive indices \!\(\*SubscriptBox[\(n\), \(i\)]\), and thin film layer thicknesses \!\(\*SubscriptBox[\(d\), \(i\)]\).  Eq. 15";
AbelesSIv::usage="AbelesSIv[\"pol\",\[Omega],{{\!\(\*SubscriptBox[\(\[Theta]\), \(0\)]\),\!\(\*SubscriptBox[\(n\), \(0\)]\)},{\!\(\*SubscriptBox[\(\[Theta]\), \(1\)]\),\!\(\*SubscriptBox[\(n\), \(1\)]\),\!\(\*SubscriptBox[\(d\), \(1\)]\)}..{\!\(\*SubscriptBox[\(\[Theta]\), \(v - 1\)]\),\!\(\*SubscriptBox[\(n\), \(v - 1\)]\),\!\(\*SubscriptBox[\(d\), \(v - 1\)]\)},{\!\(\*SubscriptBox[\(\[Theta]\), \(v\)]\),\!\(\*SubscriptBox[\(n\), \(v\)]\)}},v] calculates the partial system transfer matrix for subsystem I at layer v for frequency \[Omega] with specified material refaction angles \!\(\*SubscriptBox[\(\[Theta]\), \(i\)]\), refractive indices \!\(\*SubscriptBox[\(n\), \(i\)]\), and thin film layer thicknesses \!\(\*SubscriptBox[\(d\), \(i\)]\).  Eq. 21";
AbelesSIIv::usage="AbelesSIIv[\"pol\",\[Omega],{{\!\(\*SubscriptBox[\(\[Theta]\), \(v\)]\),\!\(\*SubscriptBox[\(n\), \(v\)]\)},{\!\(\*SubscriptBox[\(\[Theta]\), \(v + 1\)]\),\!\(\*SubscriptBox[\(n\), \(v + 1\)]\),\!\(\*SubscriptBox[\(d\), \(v + 1\)]\)}..{\!\(\*SubscriptBox[\(\[Theta]\), \(k\)]\),\!\(\*SubscriptBox[\(n\), \(k\)]\),\!\(\*SubscriptBox[\(d\), \(k\)]\)},{\!\(\*SubscriptBox[\(\[Theta]\), \(k + 1\)]\),\!\(\*SubscriptBox[\(n\), \(k + 1\)]\)}},v] calculates the partial system transfer matrix for subsystem II at layer v for frequency \[Omega] with specified material refaction angles \!\(\*SubscriptBox[\(\[Theta]\), \(i\)]\), refractive indices \!\(\*SubscriptBox[\(n\), \(i\)]\), and thin film layer thicknesses \!\(\*SubscriptBox[\(d\), \(i\)]\).  Eq. 22";

TransmitTopS::usage="TransmitTopS[\[CapitalSigma]] calculates the transmission coefficient for incidence from the top side through transfer matrix \[CapitalSigma], where \[CapitalSigma] can be S, SI, or SII. Eqs. 18, 27, and 40. ";
ReflectTopS::usage="ReflectTopS[\[CapitalSigma]] calculates the reflection coefficient for incidence from the top side through transfer matrix \[CapitalSigma], where \[CapitalSigma] can be S, SI, or SII. Eqs. 17 and 30.";
TransmitBottomS::usage="TransmitBottomS[\[CapitalSigma]] calculates the transmission coefficient for incidence from the bottom side through transfer matrix \[CapitalSigma], where \[CapitalSigma] can be S, SI, or SII.  Eqs. 20, 29, and 39.";
ReflectBottomS::usage="ReflectBottomS[\[CapitalSigma]] calculates the reflection coefficient for incidence from the bottom side through transfer matrix \[CapitalSigma], where \[CapitalSigma] can be S, SI, or SII. Eqs. 19 and 28.";

InternalTransferC::usage="InternalTransferC[\"method\",\"xPosDir\",\"inPosDir\",\!\(\*SubscriptBox[\(SI\), \(v\)]\),\!\(\*SubscriptBox[\(PhaseM\), \(v\)]\),\!\(\*SubscriptBox[\(SII\), \(v\)]\)] calculates the internal transfer coefficient for an externally incident wave with \"xPosDir\" position and directionality to an internal wave with \"inPosDir\" position and directionality adjacent to an interface.  Eqs. 23-26 and 31-38. 

\"method\"= \"SII\" (Eqs. 23-26) or \"PartialSTC\" (Eqs. 31-38)
\"xPosDir\" = \"0-\" or \"kp1+'\"
\"inPosDir\" = \"v-'\" or \"v+'\" for \!\(\*SubscriptBox[\(SI\), \(v\)]\) \!\(\*SubscriptBox[\(Phi\), \(v\)]\) \!\(\*SubscriptBox[\(SII\), \(v\)]\) or
\"inPosDir\" = \"v-\" or \"v+\" for \!\(\*SubscriptBox[\(SI\), \(v - 1\)]\) \!\(\*SubscriptBox[\(Phi\), \(v - 1\)]\) \!\(\*SubscriptBox[\(SII\), \(v - 1\)]\)";


ExternalTransferC::usage="ExternalTransferC[\"inPosDir\", \"xPosDir\", \!\(\*SubscriptBox[\(SI\), \(v\)]\), \!\(\*SubscriptBox[\(Phi\), \(v\)]\), \!\(\*SubscriptBox[\(SII\), \(v\)]\)] calculates the external transfer coefficient for a wave generated at intervace v.  Eqs. 41-44.

\"xPosDir\" = \"0+\" or \"kp1-'\" depending on which side of the system the detector lays.
\"inPosDir\" = \"v+\" for \!\(\*SubscriptBox[\(SI\), \(v - 1\)]\) \!\(\*SubscriptBox[\(PhaseM\), \(v - 1\)]\) \!\(\*SubscriptBox[\(SII\), \(v - 1\)]\)
\"inPosDir\" = \"v-'\" for \!\(\*SubscriptBox[\(SI\), \(v\)]\) \!\(\*SubscriptBox[\(PhaseM\), \(v\)]\) \!\(\*SubscriptBox[\(SII\), \(v\)]\)";

